The Rigid Pham-Brieskorn Threefolds

2023/12/11 by Michael Chitayat, Adrien Dubouloz, Chitayat, Michael +1
Mathematics · #Geometric and Algebraic Topology #Algebraic Geometry and Number Theory #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2312.07587

Abstract

We show that a 3-dimensional Pham-Brieskorn hypersurface \ X₀^a₀ + X₁^a₁ + X₂^a₂ + X₃^a₃=0\ in \mathbbA⁴ such that min\a₀, a₁, a₂, a₃ \ ≥ 2 and at most one element i of \0,1,2,3\ satisfies a_i = 2 does not admit a non-trivial action of the additive group \mathbbG_a.

Citations

• Locally Nilpotent Derivations of Graded Integral Domains and Cylindricity
• Rigidity of Graded Integral Domains and of their Veronese Subrings

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